Method for Coding a Data Stream

ABSTRACT

The invention relates to a method for coding a data stream (DS), wherein the data stream (DS) comprises a multiplicity of characters which are symbols (S) from an alphabet, wherein the characters of the data stream (DS) are combined to form a plurality of blocks (B), and the blocks (B) are entropy-coded on the basis of a code table (CT) valid for the respective block (B). The method according to the invention is characterized by the fact that the blocks (B), by means of iteration (IT), are associated with a plurality of clusters (CL) on the basis of a clearance (d) which is defined such that the clearance (d) between a block (B) and a cluster (CL) is smaller the less pronounced the change in the entropy (ET) of the cluster (CL) when adding the block (B) to the cluster (CL). In a respective iteration step, of the iteration (IT), reassignment of the blocks (B) to the clusters (CL) takes place by virtue of the blocks (B) being assigned in each case to the cluster (CL) with the smallest clearance (d) between the block (B) and the cluster (CL). Then, in each case one code table (CT) is assigned to the clusters (CL) determined by the iteration (IT), which code table is determined on the basis of the frequency distribution of the symbols (S) in at least some of the blocks (B) contained in the respective cluster (CL) and is valid for all blocks (B) of the respective cluster (CL).

The invention relates to a method for coding a data stream comprising a multiplicity of characters which are symbols from an alphabet, and to a corresponding coding device and a transmitting apparatus. The invention also relates to a method and an apparatus for transmitting a data stream.

It is known practice from the prior art to compress a data stream in a lossless manner using so-called entropy coding. In this case, relatively short codes are assigned to those symbols in the data stream which occur relatively often, with the result that the total length of the coded data stream is reduced. The corresponding symbols are assigned to codes on the basis of a code table which allocates the corresponding codes to the symbols. Since the frequency of symbols in different sections of a data stream may be different, possibly different code tables can be used for different sections or blocks of the data stream. Since the code tables must be transmitted to the corresponding decoder in order to decode the data stream, it is desirable to suitably restrict the number of said tables. There is therefore the need to efficiently code a data stream with a restricted number of code tables.

The object of the invention is therefore to code a data stream in a lossless manner with a high compression rate using code tables.

This object is achieved by means of the independent patent claims. Developments of the invention are defined in the dependent claims.

The method according to the invention is used to code a data stream having a multiplicity of characters which are symbols from an alphabet. For example, the characters may be corresponding ASCII symbols which are represented using suitable bit sequences in the data stream. The characters in the data stream are combined to form a plurality of blocks comprising a plurality of successive characters in the data stream. In this case, the blocks are entropy-coded on the basis of a code table valid for the respective block.

Within the scope of the method according to the invention, the blocks are assigned to a plurality of clusters using an iteration on the basis of a clearance which is defined in such a manner that the clearance between a block and a cluster is smaller the smaller the change (in terms of magnitude) or increase in the entropy of the cluster when adding the block to the cluster. In this case, the blocks are reassigned to the clusters in a respective iteration step of the iteration by respectively assigning the blocks to the cluster with the shortest distance between the block and the cluster. In this case, the clearance between a block and a cluster, to which the block is currently assigned, is determined in such a manner that the clearance between the block and the cluster is determined without this block.

The above term of entropy is sufficiently well known to a person skilled in the art. Entropy is the measure of the average information content of the characters which are used in a cluster and are symbols from an alphabet. In this case, the entropy for a cluster comprising one or more blocks, which comprises a total of n characters from a set of symbols s, is defined as follows:

${{ET} = {- {\sum\limits_{s}\; {{f(s)}*{\log_{2}\left( {{f(s)}/n} \right)}}}}},$

where ET denotes the entropy; where the symbols s occurring in the cluster are summed; where f(s) denotes the frequency of the corresponding symbol s in the cluster.

In the method according to the invention, a code table is respectively assigned to the clusters determined by the iteration, which code table is determined on the basis of the frequency distribution of the symbols in at least some of the blocks contained in the respective cluster and, in particular, the symbols in all blocks contained in the respective cluster and is valid for all blocks in the respective cluster.

The method according to the invention combines blocks with a similar frequency distribution to form clusters using a suitable entropy-based clearance, with the result that lossless entropy coding with high compression efficiency is achieved using accordingly determined code tables for the blocks in a cluster. In this case, the clustering is achieved on the basis of an iteration which is based on the k-means algorithm which is known from the prior art and is now used for the first time with an entropy-based clearance in the field of data coding.

In one particularly preferred embodiment of the method according to the invention, the iteration is initialized in such a manner that a plurality of clusters each comprising a block are determined and the remaining blocks, that is to say the blocks which have not yet been assigned to any clusters, are then respectively assigned to the cluster with the smallest clearance between the block and the cluster. In this case, the plurality of clusters correspond to k clusters (k≧2). In this case, k is the constantly predefined number of clusters to be formed and therefore corresponds to the number of code tables.

In one simple variant of the above initialization of the iteration, the plurality of clusters each comprising a block are randomly determined. However, alternatively or additionally, it is also possible for the block with the smallest entropy in the data stream to first of all be determined and for a cluster to be formed from this block, blocks whose minimum clearance from the already existing clusters is at a maximum then gradually being determined, a further cluster being formed, for a determined block, from this determined block until the number of clusters each comprising a block is present.

In another embodiment of the method according to the invention, the total entropy is determined as the sum of the entropies of all clusters in each iteration step, and the iteration is terminated if the difference between the total entropy determined in the respective iteration step and the total entropy determined in the preceding iteration step is lower than a predetermined threshold. Additionally or alternatively, a maximum number of iteration steps may be predefined as a criterion for terminating the iteration, the iteration being terminated if the maximum number of iteration steps is exceeded.

The entropy coding carried out within the scope of the method according to the invention with the aid of code tables can be based on any desired lossless coding method. In one preferred variant, the entropy coding is carried out using the Huffman coding which is known per se.

The method according to the invention can be used to code any desired data streams. In one variant of the invention, the data stream contains software update data, in particular for a mobile telephone. These data can be used to bring the software of a corresponding device up to date. In this case, the software update data preferably contain the difference between the old software and the new up-to-date software.

In addition to the coding method described above, the invention also relates to a coding device for coding a data stream, the data stream comprising a multiplicity of characters which are symbols from an alphabet, the characters in the data stream being combined to form a plurality of blocks. The coding device is intended to subject the blocks to entropy coding on the basis of a code table valid for the respective block.

The coding device according to the invention comprises a first means for assigning the blocks to a plurality of clusters using an iteration on the basis of a clearance which is defined in such a manner that the clearance between a block and a cluster is smaller the smaller the increase in the entropy of the cluster when adding the block to the cluster, the blocks being reassigned to the clusters in a respective iteration step of the iteration by respectively assigning the blocks to the cluster with the smallest clearance between the block and the cluster. The coding device also comprises a second means for respectively assigning a code table to the clusters determined by the iteration, which code table is determined using the second means on the basis of the frequency distribution of the symbols in at least some of the blocks contained in the respective cluster and, in particular, the symbols in all blocks contained in the respective cluster and is valid for all blocks in the respective cluster.

The coding device according to the invention is preferably configured in such a manner that one or more of the preferred variants of the method according to the invention can be carried out using the coding device.

The invention also relates to a method for emitting a data stream, the data stream being coded using the method according to the invention described above. The coded data stream and the accordingly determined code tables for the plurality of clusters and the information relating to the blocks for which the code tables are valid are then emitted.

The invention also relates to a transmitting apparatus for emitting a data stream, comprising the coding device according to the invention described above and a means for emitting the data stream coded using the coding device and the code tables for the plurality of clusters and the information relating to the blocks for which the code tables are valid.

The invention also relates to a method for transmitting a data stream, the data stream being emitted using the transmitting method according to the invention described above and being received by a receiving apparatus which decodes the coded data stream with the aid of the code tables for the plurality of clusters and the information relating to the blocks for which the code tables are valid.

The invention also relates to an apparatus for transmitting a data stream, comprising the above-described transmitting apparatus according to the invention for emitting the data stream and a receiving apparatus with a receiving means for receiving the coded data stream and the code tables for the plurality of clusters and the information relating to the blocks for which the code tables are valid. The receiving apparatus also comprises a decoding device for decoding the coded data stream with the aid of the code tables and the information relating to the blocks for which the code tables are valid.

Exemplary embodiments of the invention are described in detail below using the accompanying figures,

in which:

FIG. 1 shows a schematic illustration of the determination of clusters which is carried out within the scope of the method according to the invention; and

FIG. 2 shows a schematic illustration of a system in which a data stream is coded by a transmitting apparatus on the basis of the method according to the invention and is emitted and is then received and decoded in a receiving apparatus.

Within the scope of the embodiment of the method according to the invention described here, a data stream representing a multiplicity of characters in the form of symbols from an alphabet (for example ASCII symbols) is coded using lossless entropy coding. In this case, a plurality of successive characters in the data stream are combined to form blocks, each block being entropy-coded using a corresponding code table. In this case, corresponding code words are assigned to the symbols using the block's code table on the basis of the frequency distribution of the symbols. That is to say, the less often a symbol occurs in the corresponding block the shorter the code word. This lossless entropy coding is known per se from the prior art and Huffman coding is used in one preferred embodiment. It is now essential to the invention that a plurality of blocks with a similar frequency distribution are combined in a suitable manner to form clusters and a code table is always created only for a respective cluster. This makes it possible to achieve efficient coding with maximum compression.

The assignment of the individual blocks in the data stream to clusters is described below using FIG. 1. As the input variable, the data stream DS is processed, said data stream containing corresponding characters in the form of symbols S which are combined to form a plurality of blocks B. Within the scope of the method described here, a corresponding clearance d and an entropy ET are taken into account and are used to assign blocks to clusters, as explained in more detail below. The assignment of the blocks to clusters is based on the k-means algorithm which is known from the prior art and is used for the first time in the field of entropy coding and on the basis of a special, entropy-dependent clearance.

The aim of the k-means algorithm is generally to minimize the sum of the distances between objects and the centroid of their respective cluster. For this purpose, in a plurality of iteration steps, each object is assigned to that cluster whose centroid is closest. At the end of each iteration step, the cluster centroids (average value of the corresponding objects in the cluster) are recalculated. A suitable distance definition is required for this purpose. Within the scope of the method according to the invention, the objects are now represented by the corresponding blocks in the data stream to be coded and the distance is defined on the basis of the increase in terms of magnitude in the entropy of a cluster when adding a block to the cluster. Blocks having a similar frequency distribution of the symbols are combined using such an entropy-based distance function, with the result that the use of the same code table for blocks in a cluster results in particularly good compression.

The entropy of a block or a cluster is a variable which is sufficiently well known from the prior art and is a lower limit for the compressibility of the corresponding symbols in the block or cluster. In the case of a high entropy value, all of the symbols occurring in the block or cluster have a similar frequency. In contrast, in the case of a low entropy value, few symbols occur with great frequency.

Mathematically, the entropy ET of a block or a cluster comprising n characters each represented by a corresponding symbol s can be described as follows on the basis of the frequency f(s) of a symbol s contained in the block or cluster:

$\begin{matrix} {{ET} = {- {\sum\limits_{s}\; {{f(s)}*{{\log \left( {{f(s)}/n} \right)}.}}}}} & (1) \end{matrix}$

Here and below, log denotes the logarithm to the base 2. In this case, all of the symbols s occurring in the block or cluster are summed. In a manner equivalent to this equation, the entropy can also be written as follows:

$\begin{matrix} {{ET} = {{n\; {\log (n)}} - {\sum\limits_{s}\; {{f(s)}*{{\log \left( {f(s)} \right)}.}}}}} & (2) \end{matrix}$

If a block b comprising n_(b) characters is now added to a cluster c comprising n_(c) characters, the combined entropy increases by the following amount:

$\begin{matrix} {\delta_{c,b} = {{\left( {n_{c} + n_{b}} \right){\log \left( {n_{c} + n_{b}} \right)}} - {\left( n_{c} \right){\log \left( n_{c} \right)}} - {\sum\limits_{s_{b}}\; {\left( {{\left( {{f_{c}\left( s_{b} \right)} + {f_{b}\left( s_{b} \right)}} \right){\log \left( {{f_{c}\left( s_{b} \right)} + {f_{b}\left( s_{b} \right)}} \right)}} - {{f_{c}\left( s_{b} \right)}{\log \left( {f_{c}\left( s_{b} \right)} \right)}}} \right).}}}} & (3) \end{matrix}$

f_(b)(s_(b)) corresponds to the frequency of a corresponding symbol s_(b) occurring in block b in block b and f_(c)(s_(b)) corresponds to the frequency of a corresponding symbol s_(b) occurring in block b in cluster c. In this case, the last term from the above equation is dispensed with if f_(c)(s_(b))=0. The above variable δ_(c,b) represents the change in the entropy of a cluster c when adding the block b to the cluster c and is one embodiment of a clearance in the sense of the patent claims. In FIG. 1, this clearance is denoted by reference symbol d. The clearance δ_(c,b) just described is used in the iteration according to the k-means algorithm described further below.

According to FIG. 1, before the iteration IT based on the k-means algorithm is actually carried out, a suitable initialization is carried out in steps S1 and S2. On the basis of a predefined number k of code tables to be created, k clusters each comprising an individual block are first of all formed in the first step S1 of the initialization. In the embodiment described here, a search is carried out in this case for those blocks which are far apart from one another according to the above clearance δ_(c,b). In this case, a search is first of all carried out for that block in the data stream which has the smallest entropy. This block forms the first cluster. A search is then carried out (k−1) times for a block whose minimal distance to clusters which have already been formed is at a maximum. A new cluster is formed from this block.

Step S1 just described and also the further method steps are represented below by suitable pseudo codes. Comments in the pseudo codes are represented by two forward slashes. The entropy variable (b) in the pseudo codes corresponds to the entropy ET defined above for a corresponding block b. The distance variable (b, c) likewise corresponds to the clearance d or δ_(c,b) between a block b and a cluster c, as defined above.

The pseudo code for the above step S1 is as follows:

  Create list of free blocks which have not been assigned to any clusters; min_entropy = ∞; for all blocks b from the list {   e = entropy (b);   if (e < min_entropy) {    min_entropy = e;    min_block = b;   } } Create cluster c₁ containing block min_block; Delete min_block from the list of free blocks; max_dist = 0; for (i = 2 to k) {   //Find free block from the list with maximum   //smallest clearance from the clusters:   for all free blocks b {   //Find smallest clearance from the clusters:    min_dist = ∞;    for all clusters c {     d = distance (b, c);     if (d < min_dist) {       min_dist = d;       min_block = b;       }    }    if (min_dist > max_dist) {      max_dist = min_dist;      max_block = min_block;    }   }   Create cluster c_(i) containing block max_block;   Delete max_block from list of free blocks; } k clusters each with a block are therefore obtained after carrying out step S1. In step S2, the remaining blocks which have not yet been assigned to clusters are now allocated to the cluster with the smallest clearance from the respective block. This is achieved on the basis of the following pseudo code:

  min_dist = ∞; for all free blocks b {   for all clusters c {    d = distance (b, c);    if (d < min_dist) {     min_dist = d;     min_cluster = c;    }   }   Add block b to the cluster min_cluster; }

Step S2 is finally followed by the actual iteration IT. In this case, the blocks are reassigned to the clusters in each iteration step by determining, for each block, the closest cluster on the basis of the entropy-based clearance and shifting said block to this cluster. In order to determine the clearance between a block and the cluster in which the block is currently situated, the clearance between the block and the cluster when the block is removed from the cluster is determined in this case. After a respective iteration step has been carried out, the clusters have changed, with the result that differences in the assignment of the blocks to the clusters may arise in the next iteration step.

The iterative reassignment of the blocks to clusters can be represented by the following pseudo code, in which case the while loop below is run through as long as the variable “change” is set to the state “true”:

  change = true; iter = 0; while (change) {   change = false;   iter = iter + 1;   Calculate total entropy old_entropy;   for all blocks b {    old_cluster = cluster of b;    min_dist = ∞;    for all clusters c {     d = distance (b, c);     if (d < min_dist) {       min_dist = d;       min_cluster = c;     }    }    if (min_cluster != old_cluster) {     Shift block b from the old_cluster to     new_cluster;     change = true;    }   }   Calculate total entropy new_entropy;   if (|new_entropy - old_entropy| < epsilon || iter >   max_iter) change = false; }

In the above pseudo code, the total entropy is determined on the basis of the sum of the entropies of all clusters determined in the respective iteration step. In this case, new entropy represents the total entropy determined in the current iteration step and old entropy represents the total entropy determined in the preceding iteration step. The entropy which is determined in the current iteration step and is denoted TE in FIG. 1 is used as a criterion for terminating the iteration IT, which is indicated by the arrow P in FIG. 1. If this current entropy differs from the total entropy of the preceding iteration step by less than a predetermined threshold value (denoted “epsilon” in the pseudo code), the iteration IT is ended since there are no or only slight changes in the total entropy. A maximum number of iterations max_iter is used as a further terminating criterion according to the above pseudo code. If this maximum number of iterations is exceeded, the iteration IT is likewise terminated.

A number of k clusters denoted CL in FIG. 1 is obtained as the result of the method described above. In this case, corresponding blocks from the data stream are assigned to each cluster. All blocks which belong to the same cluster are entropy-coded using the same code table. Consequently, in a next step of the method which is no longer shown in FIG. 1, code tables are created in a manner known per se on the basis of the frequency distributions of the symbols in the blocks belonging to a respective cluster, which code tables are generally denoted CT in FIG. 1. These code tables are then used to assign code words to the symbols in the blocks, thus achieving the entropy coding of the data stream. The coded data stream can then be transmitted, together with the code tables and the assignments of the blocks to the code tables, via a corresponding transmission path and can be decoded by a receiver with the aid of the code tables and the corresponding assignment of the blocks to the tables. A corresponding scenario is illustrated in FIG. 2.

FIG. 2 shows a system according to which the original data stream DS is coded, is transmitted via a transmission path and is then decoded. In this case, the data stream DS is processed by a transmitting apparatus SE. This transmitting apparatus SE comprises a coding device CM with corresponding means M1 and M2 for carrying out the method according to the invention. In the means M1, the corresponding clusters are determined within the scope of the iteration described above. In the means M2, the suitable code tables are then determined on the basis of the frequency distributions of the symbols in the clusters and are assigned to the corresponding blocks. These code tables are then used to carry out the entropy coding in the coding device CM. The coded data stream CD produced thereby is then emitted, together with an item of additional information IN, via a corresponding transmitting means SM of the transmitting apparatus SE and is transmitted via a transmission path U. The transmitting means SM may comprise, for example, an antenna, with the result that the coded data stream CD and the information IN are wirelessly transmitted. The information IN contains the accordingly determined code tables and the assignment of the blocks in the data stream to the code tables.

The data stream CD and the information IN are finally received by a receiving apparatus RE via a corresponding receiving means RM. In the case of wireless transmission, the receiving means may comprise a corresponding receiving antenna. The coded data stream is then decoded in a decoding device DM using the code tables contained in the information IN and their assignment to the blocks. Finally, the original data stream DS is obtained again, which data stream can be recovered in a lossless manner on account of the entropy coding.

The above-described variants of the method according to the invention have a number of advantages. Blocks to be coded in the data stream are combined to form clusters with a similar frequency distribution of the symbols using a suitable entropy-based clearance. This can achieve efficient entropy coding of the data stream using corresponding code tables determined for the clusters. In this case, the determination of the clusters is based on a k-means method which has previously not been used in the field of data coding. In comparison with conventional methods in which the data stream is coded with a previously generated set of code tables, better compression results can be achieved. 

1. A method for coding a data stream (DS), the data stream (DS) comprising a multiplicity of characters which are symbols (S) from an alphabet, the characters in the data stream (DS) being combined to form a plurality of blocks (B), and the blocks (B) being entropy-coded on the basis of a code table (CT) valid for the respective block (B), characterized in that the blocks (B) are assigned to a plurality of clusters (CL) using an iteration (IT) on the basis of a clearance (d) which is defined in such a manner that the clearance (d) between a block (B) and a cluster (CL) is smaller the smaller the change in the entropy (ET) of the cluster (CL) when adding the block (B) to the cluster (CL), the blocks (B) being reassigned to the clusters (CL) in a respective iteration step of the iteration (IT) by respectively assigning the blocks (B) to the cluster (CL) with the smallest clearance (d) between the block (B) and the cluster (CL); a code table (CT) is respectively assigned to the clusters (CL) determined by the iteration (IT), which code table is determined on the basis of the frequency distribution of the symbols (S) in at least some of the blocks (B) contained in the respective cluster (CL) and is valid for all blocks (B) in the respective cluster (CL).
 2. The method as claimed in claim 1, characterized in that the iteration (IT) is initialized in such a manner that a plurality of clusters (CL) each comprising a block are determined and the remaining blocks (B) are then respectively assigned to the cluster (CL) with the smallest clearance (d) between the block (B) and the cluster (CL).
 3. The method as claimed in claim 2, characterized in that the plurality of clusters (CL) each comprising a block (B) are randomly determined when initializing the iteration (IT).
 4. The method as claimed in claim 2 or 3, characterized in that the block (B) with the smallest entropy (ET) in the data stream (DS) is first of all determined when initializing the iteration and a cluster (CL) is formed from this block (B), blocks (B) whose minimum clearance (d) from the already existing clusters (CL) is at a maximum then gradually being determined, a further cluster (CL) being formed, for a determined block (B), from this determined block (B) until the plurality of clusters (CL) each comprising a block (B) are present.
 5. The method as claimed in one of the preceding claims, characterized in that the total entropy (TE) is determined as the sum of the entropies of all clusters (CL) in each iteration step, and the iteration (IT) is terminated if the difference between the total entropy (TE) determined in the respective iteration step and the total entropy (TE) determined in the preceding iteration step is lower than a predetermined threshold.
 6. The method as claimed in one of the preceding claims, characterized in that the iteration (IT) is terminated if a maximum number of iteration steps is exceeded.
 7. The method as claimed in one of the preceding claims, characterized in that the blocks (B) are entropy-coded using Huffman coding.
 8. The method as claimed in one of the preceding claims, characterized in that the data stream (DS) comprises software update data, in particular for a mobile radio telephone.
 9. A coding device for coding a data stream, the data stream (DS) comprising a multiplicity of characters which are symbols (S) from an alphabet, the characters in the data stream (DS) being combined to form a plurality of blocks (B), the coding device (CM) being intended to subject the blocks (B) to entropy coding on the basis of a code table (CT) valid for the respective block (B), characterized in that the coding device (CM) comprises: a first means (M1) for assigning the blocks (B) to a plurality of clusters (CL) using an iteration on the basis of a clearance (d) which is defined in such a manner that the clearance (d) between a block (B) and a cluster (CL) is smaller the smaller the change in the entropy (ET) of the cluster (CL) when adding the block (B) to the cluster (CL), the blocks (B) being reassigned to the clusters (CL) in a respective iteration step of the iteration (IT) by respectively assigning the blocks (B) to the cluster (CL) with the shortest distance (d) between the block (B) and the cluster (CL); a second means (M2) for respectively assigning a code table (CT) to the clusters (CL) determined by the iteration (IT), which code table is determined using the second means (M2) on the basis of the frequency distribution of the symbols (S) in at least some of the blocks (B) contained in the respective cluster (CL) and is valid for all blocks (B) in the respective cluster (CL).
 10. The coding device as claimed in claim 9, which is designed to carry out a method as claimed in one of claims 2 to
 8. 11. A method for emitting a data stream (DS), characterized in that the data stream (DS) is coded using a method as claimed in one of claims 1 to 8 and the coded data stream (CD) and the code tables (CT) for the plurality of clusters (CL) and the information relating to the blocks (B) for which the code tables (CT) are valid are emitted.
 12. A transmitting apparatus for emitting a data stream (DS), comprising a coding device (CM) as claimed in claim 9 or 10 and a means (SM) for emitting the data stream (CD) coded using the coding device (CM) and the code tables (CT) for the plurality of clusters (CL) and the information relating to the blocks (B) for which the code tables (CT) are valid.
 13. A method for transmitting a data stream, characterized in that the data stream (DS) is emitted using the method as claimed in claim 11 and is received by a receiving apparatus (RE) which decodes the coded data stream (CD) with the aid of the code tables (CT) for the plurality of clusters (CL) and the information relating to the blocks (B) for which the code tables (CT) are valid.
 14. An apparatus for transmitting a data stream (DS), comprising a transmitting apparatus (SE) as claimed in claim 12 for emitting the data stream (DS) and a receiving apparatus (RE) with a receiving means (RM) for receiving the coded data stream (CD) and the code tables (CT) for the plurality of clusters (CL) and the information relating to the blocks (B) for which the code tables (CT) are valid, and having a decoding device (DM) for decoding the coded data stream (CD) with the aid of the code tables (CT) and the information relating to the blocks (B) for which the code tables (CT) are valid. 